arXiv subjects

Abhay Kumar Singh

Publications and source records attributed to Abhay Kumar Singh.

23 records · Page 2Linked to original sources

arXiv2015

On cyclic DNA codes over the Ring $\Z_4 + u \Z_4$

In this paper, we study the theory for constructing DNA cyclic codes of odd length over $\Z_4[u]/\langle u^2 \rangle$ which play an important role in DNA computing. Cyclic codes of odd length over $\Z_4 + u \Z_4$ satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The structure and existence of such codes are also studied. The paper concludes with some DNA example obtained via the family of cyclic codes.

cs.IT↗

arXiv2015

A class of cyclic Codes Over the Ring $\Z_4[u]/ $ and its Gray image

Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their $\Z_2$ image. Making use of algebraic structure, we find the some good $\Z_2$ codes of length 28.

cs.IT↗

arXiv2015

On cyclic self-orthogonal codes over Zpm

The purpose of this paper is to study the cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$. After providing the generator polynomial of cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$, we give the necessary and sufficient condition for the existence of non-trivial self orthogonal codes over $\mathbb{Z}_{p^m}$ . We have also provided the number of such codes of length $n$ over $\mathbb{Z}_{p^m}$ for any $ (p,n) = 1 $.

cs.IT↗

arXiv2015

On Coretractable Module

The main aim of this paper is to discuss the structure of coretractble and mono-coretractble modules. We have provided the characterizations of coretractable modules in terms of Kasch ring, CS modules, mono-coretractble modules, projective modules, epi retractable modules, and retractable modules. We have also discussed some equivalent condition related with coretractbele and mono-coretractble modules.

math.RA↗

arXiv2012

On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$

In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.

cs.IT↗